Relations and F...

$$p \Rightarrow \,q$$ can also be written as 

If $$R$$ is relation is "greater then or equal" from $$A=\left\{1,2,3,4\right\}$$ to $$B=\left\{4,5,6\right\}$$, then $$R^{-1}=$$

The domain of the function $$f(x)=log_5\left(log_4{log_{4/\pi }(tan^{-1})^{-1}}\right)$$ is 

The number of ordered pairs (x, y) of natural numbers satisfy the equation $$x^2+y^2+2xy-2018x-2018y-2019^o=0$$ is?

Let $$p(x)=ax^{2}+bx  \ ,q(x)=\ell x^{2}+mx+n$$ and consider a function $$f(x)=p(x)-q(x)$$. If $$f(x)=0$$ only for $$x=1$$ and $$f(2)=1$$ then, the value of $$f(3)$$ is:

The number of dissimilar terms in the expansion of $$(a+b+c)^{n}$$ is 

If the relation $$R:A \to B$$ where $$A = \left\{ {1,2,3,4} \right\},B = \left\{ {1,3,5} \right\}$$ is defined by $$R = \left\{ {\left( {x,y} \right):x < y,x \in A,y \in B} \right\}$$ then $$Ro{R^{ - 1}} = $$ 

Let $$f\left( x \right) =\dfrac { C\quad tanx-{ c }^{ x }+ln(sicx\_ tanx)-x }{ Tan\quad x-x }$$ 
be a continuous function at x=0.
The value of f(0) equals ________.

Let $$f ( x ) = a x ^ { 2 } + b x + c \text { with } f ( - 1 ) < 1 , f ( 1 ) > - 1 , f ( 3 ) < - 4$$ and $$a \neq 0$$ then

If $$ \int f(x) \, cos x \, dx = \dfrac{1}{2} f^2(x) + c$$ then f(x) is